Algebra worksheet — GCSE Foundation

1.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

2.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

3.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

4.A curve has equation y = x² − 9. Which statement about its graph is correct?

5.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

6.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

7.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

8.Which expression is equivalent to 3(2x − 5) + 4x?

9.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

10.Solve x² − 6x = 0.

11.Solve 4x + 3 = 19

12.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

13.Solve the inequality 5 − x ≤ 2.

14.Which expression means the same as 3 × a × b?

15.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.